If y varies directly as x and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this relation?

The  numeric constant of variation in this relation is 40

If y varies directly as x, this is expressed as;

k is the constant of proportionality

If y is 400 when x is r, then;

400 = kr

k = 400/r .................. 1

If y is r when x is 4, then;

r = 4k

k = r/4 ............................2

Equate equation 1 and 2

400/r = r/4

r² = 1600

r = √1600

r = 40

Hence the  numeric constant of variation in this relation is 40

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